Kevin Davey
University of Chicago
In [7] and [8], it is established that given any abstract countable structure S and a relation R on S, then as long as S has a recursive copy satisfying extra decidability conditions, R will be ∑0α on every recursive copy of S iff R is definable in S by a special type of infinitary formula, a ∑rα() formula. We generalize the typ e of constructions of these papers to produce conditions under which, given two disjoint relations R1 and R2 on S, there is a recursive copy of S in which R1 and R2 are 0α inseparable. We then apply these theorems to specific everyday structures such as linear orderings, boolean algebras andvector spaces
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DOI 10.1016/0168-0072(94)90046-9
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References found in this work BETA

Pairs of Recursive Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.
Stability of Recursive Structures in Arithmetical Degrees.C. J. Ash - 1986 - Annals of Pure and Applied Logic 32:113-135.
Categoricity in Hyperarithmetical Degrees.C. J. Ash - 1987 - Annals of Pure and Applied Logic 34 (1):1-14.
Intrinsically Gs;0alpha; Relations.E. Barker - 1988 - Annals of Pure and Applied Logic 39 (2):105-130.
Pairs of Computable Structures.C. J. Ash & J. F. Knight - 1990 - Annals of Pure and Applied Logic 46 (3):211-234.

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